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Optimal Time Series Forecasting Through the GARMA Model

Author

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  • Adel Hassan A. Gadhi

    (School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
    Institute of Public Administration, Department of Digital Transformation and Information, Riyadh 11141, Saudi Arabia)

  • Shelton Peiris

    (School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia)

  • David E. Allen

    (School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
    School of Business and Law, Edith Cowan University, Joondalup, WA 6027, Australia
    Department of Finance, Asia University, Taichung 41354, Taiwan)

  • Richard Hunt

    (School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia)

Abstract

This paper examines the use of machine learning methods in modeling and forecasting time series with long memory through GARMA. By employing rigorous model selection criteria through simulation study, we find that the hybrid GARMA-LSTM model outperforms traditional approaches in forecasting long-memory time series. This characteristic is confirmed using popular datasets such as sunspot data and Australian beer production data. This approach provides a robust framework for accurate and reliable forecasting in long-memory time series. Additionally, we compare the GARMA-LSTM model with other implemented models, such as GARMA, TBATS, ARIMA, and ANN, highlighting its ability to address both long-memory and non-linear dynamics. Finally, we discuss the representativeness of the datasets selected and the adaptability of the proposed hybrid model to various time series scenarios.

Suggested Citation

  • Adel Hassan A. Gadhi & Shelton Peiris & David E. Allen & Richard Hunt, 2025. "Optimal Time Series Forecasting Through the GARMA Model," Econometrics, MDPI, vol. 13(1), pages 1-23, January.
    • Handle: RePEc:gam:jecnmx:v:13:y:2025:i:1:p:3-:d:1562553
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    References listed on IDEAS

    as
    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Adel Hassan A. Gadhi & Shelton Peiris & David E. Allen, 2024. "Improving Volatility Forecasting: A Study through Hybrid Deep Learning Methods with WGAN," JRFM, MDPI, vol. 17(9), pages 1-20, August.
    3. Changqing Cheng & Akkarapol Sa-Ngasoongsong & Omer Beyca & Trung Le & Hui Yang & Zhenyu (James) Kong & Satish T.S. Bukkapatnam, 2015. "Time series forecasting for nonlinear and non-stationary processes: a review and comparative study," IISE Transactions, Taylor & Francis Journals, vol. 47(10), pages 1053-1071, October.
    4. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
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